Hi everyone, I'm having trouble with this question and I'm not sure how to do it/where to start. Does anyone have a solution to it? It will help me with my future problems on this topic!
Answers
This is quite an interesting problem. I am not sure how high you are in math, but I am going to use calculus I techniques to solve it. First, we need to model an equation. Let P be the total profit and x be every time you increase the cost by $10. If you think about it hard enough you come up with the equation
[tex]P(x)=(200-5x)(250+10x)[/tex]
(200-5x) is the amount of plots you will be able to sell, and (250+10x) is the amount you charge for. So, at x =0
[tex]P(0)=(200-5(0))(250+10(0))=(200)(250)=$50,000[/tex]
This is the initial condition where if we sell 200 plots at $250/plot.
So, this equation makes sense.
Now, let's maximize using the first derivative of the function.
Let's get it into an easily differentiable form.
[tex]P(x)=(200-5x)(250+10x)=-50x^2+2000x-1250x+50000\\=-50x^2+750x+50000[/tex]
From here, differentiate the problem.
[tex]P'(x)=-100x+750[/tex]
Now, set it equal to zero and solve for x.
[tex]P'(x)=-100x+750=0\\x=7.5[/tex]
This a critical point of the function. Let's plug back into the original equation to see what it gives us.
[tex]P(7.5)=(200-5(7.5))(250+10(7.5))=(162.5)(325)=52,812.50[/tex]
You cant sell half a plot, so we need to see what happens if we sell 162 plots and 163 plots, and then compare which one gives us more money.
In order to sell 162 plots
[tex]200-5x=162\\x=7.6[/tex]Plug back into P(x) to see the profit
[tex]P(7.6)=(200-5(7.6))(250+10(7.6))=(162)(326)=52,812[/tex]
Now, do the same for 163 plots
[tex]200-5x=163\\x=7.4\\P(7.4)=(200-5(7.4))(250+10(7.4))=(163)(324)=52,812[/tex]
As we can see, they are the same. So, you can charge either $324 or $326 in rent. But, if your teacher is not looking for a logical answer and you can somehow sell half a plot, you can charge $325 in rent for the maximum profit.
Related Questions
Rico had $80. He spent 40% on snacks and 1/4 on travel and kept 1/2 of the remainder for the next day.
Answers
Answer:
$4????
Step-by-step explanation:
I searched 40% of 80 and got 32, then 1/4 of 32, which was 8, then that in half was 4. I am not sure if it is right or if 8 was the final answer.
(1/2)power 5=?? please help
Answers
[tex] \frac{1}{2} \: to \: the \: power \: of \: 5 \: is \: \frac{1}{32} or \: 0.03125 [/tex]
Answer:
[tex] \ {\boxed{ \tt ( \frac{1}{2}) ^{5} = \frac{1}{32} }}[/tex]
Step-by-step explanation:
[tex] \\ \tt( \frac{1}{2} )^{5} [/tex]
[tex] \\ \tt= \frac{ {1}^{5} }{ {2}^{5} } [/tex]
[tex] \\ \tt = \frac{1 \times 1 \times 1 \times 1 \times 1}{2 \times 2 \times 2 \times 2 \times 2} [/tex]
[tex] \\ \tt = \frac{1}{32} [/tex]
If an item that originally cost $12 is increased to $16, what is the percentage of increase in the item?
Answers
[tex] \rightarrow [/tex] 12.5%
=================================================
Explanation/Solution:To solve, use the formula:
[tex] \rightarrow \: \rm Percent \: of \: Increase = \frac{Amount \: of \: Increase}{Original \: Amount} \\ [/tex]
Solve.
[tex] \rightarrow \: \rm = \frac{16 - 12}{12} [/tex] Amount of increase: 16 - 12 = 2
[tex] \rightarrow \: \rm = \frac{2}{16} [/tex] Simplify.
[tex] \rightarrow \: \rm = \frac{x}{100} = \frac{1}{8}[/tex] Write the fraction as a percent.
[tex] \rightarrow [/tex]8x = 100 Find the product of the extreme and the means.
[tex] \rightarrow \: \rm = \frac{8x}{8} = \frac{100}{8}[/tex] Divide both sides by 8.
[tex] \rightarrow [/tex]x = 12.5
Therefore, the percentage of increase in the item is 12.5%.
The total amount of snowfall last ski season was 50 inches. This season, the total amount was 56 inches. The
percent of snowfall this year is what compared to last year?
Answers
Answer:
12% increase compared to last years
Step-by-step explanation:
A teacher categorized students by whether they regularly completed their homework (or not) and whether they passed the course (or not). The data are in the table below.
Completed Homework Did not Complete Homework Total
Passed the Course 25 7 32
Did not Pass the Course 5 18 23
Total 30 25 55
A student from the class is randomly selected. Determine the following probabilites. Enter your results as percents rounded to two decimal places.
What is the probability a student passed the course given that they completed their homework?
%
What is the probability a student passed the course given that they didn't complete their homework?
28
Correct%
What is the probability a student completed their homework given that they passed the course?
%
What is the probability a student didn't complete their homework given that they didn't pass the course?
%
Answers
Probabilities are used to determine the chances of an event.
Let P represents the event that a student passes the course, and C represents the event that a student completes the assignment
(a) The probability a student passed the course given that they completed their homework?
From the table, we have:
[tex]\mathbf{n(P\ n\ C) = 25}[/tex]
[tex]\mathbf{n(C) = 30}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(C)}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{25}{30}}[/tex]
[tex]\mathbf{Pr = 0.8333}[/tex]
Express as percentage
[tex]\mathbf{Pr = 83.33\%}[/tex]
Hence, the probability a student passed the course given that they completed their homework is 83.33%
(b) The probability a student passed the course given that they didn't complete their homework
From the table, we have:
[tex]\mathbf{n(P\ n\ C'= 7}[/tex]
[tex]\mathbf{n(C') = 25}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C')}{n(C')}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{7}{25}}[/tex]
[tex]\mathbf{Pr = 0.28}[/tex]
Express as percentage
[tex]\mathbf{Pr = 28\%}[/tex]
Hence, the probability a student passed the course given that they didn't complete their homework is 28%
(c) The probability a student completed their homework given that passed the course?
From the table, we have:
[tex]\mathbf{n(P\ n\ C) = 25}[/tex]
[tex]\mathbf{n(P) = 32}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P\ n\ C)}{n(P)}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{25}{32}}[/tex]
[tex]\mathbf{Pr = 0.78125}[/tex]
Express as percentage
[tex]\mathbf{Pr = 78.125\%}[/tex]
Approximate
[tex]\mathbf{Pr = 78.13\%}[/tex]
Hence, the probability a student completed their homework given that they passed the course is 78.13%
(d) The probability a student didn't complete their homework given that they didn't pass the course
From the table, we have:
[tex]\mathbf{n(P'\ n\ C'= 18}[/tex]
[tex]\mathbf{n(P) = 23}[/tex]
So, the required probability is:
[tex]\mathbf{Pr = \frac{n(P'\ n\ C')}{n(P')}}[/tex]
This gives
[tex]\mathbf{Pr = \frac{18}{23}}[/tex]
[tex]\mathbf{Pr = 0.7826}[/tex]
Express as percentage
[tex]\mathbf{Pr = 78.26\%}[/tex]
Hence, the probability a student didn't complete their homework given that they didn't pass the course is 78.26%
Read more about probabilities at:
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Answer the following:
a) 3-8=
b) -6 -4 =
c) -2 + 6 =
Answers
Answer:
a) =5
b) = -10
c) = 4
Step-by-step explanation:
Round off the decimal 55.345 to 2 decimal places.
Answers
Answer:
Step-by-step explanation:
55.345 is rounded off two places therefore, the hundreths place
the number next to 4 is 5 in the thousandths place. 5 is high and therefore 4 is changed to 5 and makes it 53.35
Simplify.
1) 448
A) 5V3
C) 12V2
B) 8V
D) 10v2
Answers
Answer:
B
Step-by-step explanation:
The square root of 448 rounded up to 6 decimal places is 21.166010. It is the positive solution of the equation x2 = 448. We can express the square root of 448 in its lowest radical form as 8 √7.
Hello I need help help help help
Answers
x = 16
7 times 2 = 14
8 times 2 = 16
Hope that helped:)
5 is 10% of what plz i need help
Answers
Answer:
50
Step-by-step explanation:
I will mark brainlist
Determine whether points A, B, and C can be vertices of a triangle. If so, classify the triangle as acute, right, or obtuse.
A (3,1); B (5,6); C (4,2)
Acute
Right
Obtuse
None of these
Answers
Answer:
A Obtuse, B Acute, C Right I think its right
Step-by-step explanation:
HELLOPPPPPPPPPPPPPPPP
Answers
Answer:
Hello!
Judging by the link you provided I have come up with the correct solution:
x= 61°
y= 29°
Step-by-step explanation:
I will link my work below:
The first step to finding the two solutions it to first identify one of them.
I chose to identify x first.
To identify the value of x in this problem you have to notice that the x value corresponds with the value "29°" to form a perfect right angle, being 90°.
Thus you can simply find the value of x by doing this formula:
x+29°=90°
You then subtract 29° from both sides to simplify, and you come up with the solution
x=61°
Now we need to find the value of y.
To find the value of y I noticed that again, like x, y corresponds with another variable (being x) to form a perfect right angle (90°).
The way I realized this is a perfect right angle is because, as you can see in the picture you provided, the y+x angle are alternate exterior angles with another angle that is 90°.
Thus you can assume that:
x+y=90°
x= 61°
61°+y=90°
You then subtract 61° from both sides to get:
y=29°
Consider the figures below. Which of the following statements are true, given <S is congruent to <J and <N is congruent to <E? Select all that apply.
<A is congruent to <O
Triangle SAN~TriangleJOE
Triangle SAN is congruent to Triangle JOE
SN is congruent to JE
The perimeter of Triangle JOE is half the perimeter of Triangle SAN
There exists a sequence of rigid motion that maps Triangle JOE onto Triangle SAN
There exists a sequence of rigid and non-rigid motions that maps Triangle SAN onto Triangle JOE
Answers
Answer:
<A is congruent to <O
Triangle SAN~TriangleJoe
There exists a sequence of rigid motion that maps Triangle JOE onto Triangle SAN
Step-by-step explanation:
So sorry if i am wrong!! I hope this can help!
Answer:
A
B
G
Angle A is congruent to angle O
Triangle SAN ~ Triangle JOE
There exists a sequence of rigid and non-rigid motions that maps triangle SAN onto triangle JOE
Step-by-step explanation:
Just got the question wrong, this was the correct answer
HELPPP LAST ATTEMPT!!
Answers
Hope this helped!! :)
A 4-digit number is made up of different odd digits.
Write the greatest possible number that it can be?
Answers
Answer:
9753
Step-by-step explanation:
the area of a circle in terms of pi is 4pi m2. find the value of the diameter
Answers
Answer:
4 m
Step-by-step explanation:
The area of a circle is given in terms of diameter by ...
A = (π/4)d²
Then the diameter in terms of area is ...
d = √(4A/π)
For the given area, the diameter is ...
d = √(4·4π/π) = 4 . . . meters
The diameter of the circle is 4 meters.
1
21314 JEG B 10
3
Which is the best estimate of -14
of-14; (-20)
ם
10
-42
-28
OOOO
28
42
Answers
Step-by-step explanation:
OOOO
BYE
Rewrite without parentheses and simplify.
(check my page and answer my other questions if u can please it would mean alot)
Answers
Answer:
x² +14x +49
Step-by-step explanation:
Use the distributive property and collect terms.
(x +7)² = (x +7)(x +7)
= x(x +7) +7(x +7)
= x² +7x +7x +49
= x² +14x +49
What is the relationship between the 9 in the hundreds place and the 9 in the tens place in 2,743,995?
Answers
Hundred and tenths are the relationship of 9 in the number
Answer:
The 9 in the hundreds column is ten times greater than the 9 in the tens column.
Step-by-step explanation:
The temperature at the North Pole averages -36࿁F. This past winter, the temperature averaged -47࿁F. Write a correct statement that compares the absolute values of the two temperatures
Answers
Comparing the temperature average, it can be concluded that the current average temperature is higher than the past average by 11°F
The temperature difference between the present and past winter can be expressed thus :
Current temperature average = - 36°F Past average = - 47°FTemperature difference :
-36 - (-47) = 11°FTherefore, we can conclude that the current average temperature is higher than the past average by 11°F
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HELP ME
NO BOTS
BRAINLIST TO FIRST CoRrEcT ANSWER
Answers
Answer:
The answer is A.
Step-by-step explanation:
5 - 1 = 4
10 - 6 = 4
15 - 11 = 4
20 - 16 = 4
25 - 21 = 4
Answer:
The correct answer should be B
Step-by-step explanation:
B is also number 5
(PHOTO) please help need this done by tomorrow thank you.
Answers
Answer: 125
Step-by-step explanation: ∠4 and 55 are supplementary angles. This means that ∠4 and 55 add up to 180. We can use this to solve for ∠4.
180 - 55 = ∠4
125 = ∠4
So, ∠4 is equal to 125 degrees.
Would appreciate brainly <3
A class of 22 students has taken an exam, and the mean of their scores is 76.5. One student takes the
exam late, and scores 92. After including the new score, what is the mean score for all 23 exams? Round
to the nearest hundredth.
Answers
The mean score for all 23 students is 77.17.
Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number.
The first step is to determine the total scores of the 22 students.
Total scores = mean score x number of students
22 x 76.5 = 1683
The second step is to add the score of the student that took the exam late tot he total scores.
New total score = 1683 + 92 = 1775
The third step is to determine the new mean score.
new mean score = new total score / total number of students
1775 / 23 = 77.17
To learn more about the mean of a set of numbers, please check: https://brainly.com/question/15420908?referrer=searchResults
Shawna has a photo album with space for 160 pictures. She has 33 pictures of her family, 48 pictures from summer camp, and 57 pictures from school. Does she have enough pictures to fill the photo album?
Answers
and she will be able to have 22 more photos
sincd 160-138 is 22
7x when x=3
Please help
Answers
Answer:
21
Step-by-step explanation:
7x, x=3. Plug x in as 3. 7x3=21.
A large grocery store needs to decide how many bottles of 2 liter
Dr. Pepper to stock each week in the store. The store must decide how many bottles to stock each week. The weekly demand for 2 liter Dr. Pepper follows a Normal Distribution with a mean of 550 bottles and a standard deviation of 26 bottles. The store desires that the probability that they do not run out of 2 liter bottles of Dr. Pepper in a week to be .995.
How many bottles should they stock at the beginning of the week to have a .995 probability of not running out during the week. Choose what you believe is the best answer from the following:
i) 601,
ii) 610
iii) 617
iv) 483
v) 490
vi) none of the above
Answers
Answer:
I Kinda Confused Man
Step-by-step explanation:
I Dont Even Know The Right Answer
there are 25 questions in a quiz
every correct answer scores 3 points
each incorrect answer loses 2 points
a question not answered scores o points.
it is possible to finish the quiz with a negative score
what is the minimum score you can get on the quiz ❓
Answers
Points obtained on the quiz increases when the points are earned from
correct responses.
The minimum score from the quiz is -50Reasons:
The number of questions in the quiz = 25 questions
Number of points for correct answers = 3 points
Number of points lost for incorrect answers = 2 points
Points for question not answered = 0 points
Nature of total points = Positive and negative
Required:
The minimum score one can get on the quiz.
Solution:
The minimum score that can be obtained is when all responses result in a
loss of points, due to the questions being incorrect.
Therefore;
The minimum score = 25 × (-2) = -50
Learn more here:
https://brainly.com/question/19816972
5. The price for
seedless oranges is $1.55 for the first
pound and $0.75 for each additional pound. Paul Paid $
5.35 to buy sour oranges.
How many pounds of seedless oranges did he buy?
Answers
Answer:
5 1/15 lb
Step-by-step explanation:
Equation:
5.35 = 1.55 + 0.75x [tex]\longmapsto\\[/tex] Subtract 1.55 from both sides
3.8 = 0.75x [tex]\longmapsto[/tex] Divide both sides by 0.75
5 1/15 lb
-Chetan K
What is 6/9 divided by 1/3
Answers
Answer:
2
Step-by-step explanation:
6/9÷1/3
Keep Change Flip
6/9 x 3/1
Multiply.
6/3
=2
Hope this helps :)
Answer:
2
Step-by-step explanation:
we have[tex]\frac{6/9}{1/3}[/tex] . dividing by a fraction is the same as multiplying by the reciprocal. so [tex]\frac{6/9}{1/3}[/tex]= (6/9) * 1/(1/3) = (6/9) * 3. we can also simplify 6/9 to 2/3 by taking 3 out of the numerator and denominator. now we have (2/3) * 3 which equals 2
sam's age is 125% of mary's age. mary's age is p% of sam's age. what is the value of p?
Answers
S(S+8) = 105
S^2+8S-105 = 0
(S+15)(S-7) = 0
Sam’s sister is 7 years and Sam is 15 years old.